In reversible nanocomputing, an emerging area of research is quantum dot cellular automata (QCA)-based design of cost-effective reversible nanocircuits. In a digital nanocommunication system, the router is the heart of data transmission. At nanoscale, for data communication the device density and energy dissipation of the circuit are key issues. A reversible circuit exhibits low energy dissipation or ideally no energy dissipation. This paper presents the design of a Fredkin gate- and a BJN gate-based design of reversible 4:1 multiplexer and 1:4 demultiplexer based on QCA with quantum costs of 15 and 30 respectively and garbage output of six and ten respectively. The proposed reversible multiplexer and demultiplexer are used to achieve a reversible nanorouter in QCA for the first time, with a quantum cost of 40 and garbage output of 16. The proposed reversible nanorouter could be used to achieve a nanocommunication system in the near future at the nanoscale low energy level. A QCA device is used to implement the proposed reversible circuits, to achieve a low-energy nanoscale circuit. The comparison of simulation consequences of proposed circuits with theoretical knowledge established the functional efficiency of the circuit.